Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x - 2$ and $ BC = 5x + 18$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x - 2} = {5x + 18}$ Solve for $x$ $ 4x = 20$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({5}) - 2$ $ BC = 5({5}) + 18$ $ AB = 45 - 2$ $ BC = 25 + 18$ $ AB = 43$ $ BC = 43$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {43} + {43}$ $ AC = 86$